What's weird no codes. The only time it seems that the AC doesn't work is if you leave it on turn off the car they turn the car back on sometimes the AC won't turn on however if you turn the AC off before turning off the car then turn on the car then the AC no issues.
Any thoughts

Do you have auto climate control?Or is it manual?If your getting a check engine light with no codes then they probably used a basic code reader that only reads engine and transmission codes. Not body control module air bag hvac codes etc. So you probably have codes set in another computer.

Alright you threw me off when you said it was a manual auto climate control. When the ac shuts off while driving is the car running too hot or overheating?Are the electric fans working like they should?Also I would clean all the fins on the radiator and ac condensor of all the debris that might be trapped in them. After that will be checking the high and low ac pressures.